Aerial mapping is a fast growing market for both military and civil applications. Aerial mapping acquires airborne image data using remote sensing and produces highly accurate topographic maps of ground regions of interest. Depending on the application, the topographic data produced by aerial mapping are used for evaluation of the dimensions and content of an observed target.
The ability of aerial mapping to provide comprehensive and detailed topographic information depends largely on the capabilities and features of the imaging lens that is used, including the distortion of the lens (whereby the image shape does not precisely reproduce the object shape, depending on the viewing angle), correction of monochromatic and polychromatic aberrations (including secondary spectrum), telecentricity, and thermal stability of the lens (ability to produce images over a required range of temperatures). Compactness and a wide field of view are also highly desirable.
U.S. Pat. No. 4,333,714 (Jun. 8, 1982) discloses a reverse telephoto wide angle lens for use in interchangeable photographic cameras. The '714 lens has a wide field of view, but it is far from being telecentric, it not corrected for distortion, and its secondary spectrum is quiet large. Also this lens is not athermalized and refocus of the image plane is required to compensate for the temperature change. At least for these reasons, the '714 lens is not useable for remote aerial high resolution photography and precise mapping.
Another example of a reverse telephoto lens is disclosed in U.S. Pat. No. 4,235,520 (Nov. 25, 1980). However, the '520 lens is not corrected for distortion, and has a significant field curvature and secondary spectrum. The '520 lens is also not athermalized.
A telecentric lens is disclosed in U.S. Pat. No. 6,563,650 (May 13, 2003). The '650 lens is designed to work with special beam splitters directing light onto three different LCDs. Spherical aberration is compensated in the '650 lens by the spherical aberration introduced by the beam-splitter. Distortion and secondary spectrum are not corrected.
Yet another telecentric lens is disclosed in U.S. Pat. No. 6,639,653 (Oct. 28, 2003). The '653 lens has a small numerical aperture (NA) and large overall length. However, distortion and secondary spectrum are not corrected.
Still another projection lens is disclosed in U.S. Pat. No. 6,038,078 (Mar. 14, 2000). The '078 lens is rather complicated, has a large overall length and a small field of view.
Yet another telecentric lens is disclosed in U.S. Pat. No. 5,905,596 (May 18, 1999). As with the '650 lens, spherical aberration of the '596 lens is corrected by the spherical aberration introduced by a beam-splitter, while distortion and secondary spectrum are not corrected.
Optical distortion is a function of the viewing angle. The distortion of lenses used in aerial mapping should be less than 0.5%. Such lenses should be able to operate at different altitudes, from sea level and up to 30000 feet.
The index of refraction of all optical glasses varies as a function of wavelength—this is called dispersion. When the chromatic aberration is not corrected, each wavelength is focused at a different point along the optical axis. If the optical system is achromatized over a given bandwith, the outer wavelengths of the bandwidth have a common focus. The primary axial color is the difference between the focus positions of the outer wavelengths, and should be corrected to achieve good image quality by selecting glass types and lens optical powers to compensate for the axial color.
When this state of achromatization is achieved, the primary color is corrected. The remaining chromatic aberration is referred to as secondary color. Secondary color is the difference between the focus points for the outer wavelengths of the achromatized bandwidth and the central wavelength. Secondary color is the limiting axial aberration in a lens design, and may be a dominating aberration for high resolution lenses used in aerial photography and mapping.
Monochromatic and chromatic aberrations depend on the heights and angles of rays at the optical element surface and the refraction index of the material. These aberrations also depend on the shape of the optical element, and on its location with respect to the aperture stop.
The contribution of the optical element to the total axial color is proportional to the square of axial marginal ray height at the lens, its optical power, and the reciprocal of the Abbe number of the lens material.
The Abbe number Vd is given byVd=(nd−1)/(nF′−nC′)  (1)where nd is the index of refraction of the glass at the wavelength of the helium line d (587.6 nm), nF′ is the index of refraction at the blue cadmium line F′ (479.99 nm), and nC′ is the index of refraction at the red cadmium line C′ (643.85 nm).
Accordingly, the smaller the value of Vd, the greater the chromatic dispersion of the glass.
For the achromatic (axial color corrected) doublet, the powers and the dispersions of the elements are chosen to produce zero total dispersion by combining two elements to satisfy the following equation:Φ1/V1=Φ2/V2  (2)where                Φ1=the optical power of the first element,        V1=the Abbe number of the first element,        Φ2=the optical power of the second element, and        V2=the Abbe number of the second element.        
The secondary spectrum SSdoublet for a cemented doublet of optical elements having an optical power Φ is given by:SSdoublet=[(−1/Φ)(P1−P2)]/(V1−V2)  (3)where                P1=partial dispersion of the first element, and        P2=partial dispersion of the second element.        
Partial dispersion describes dispersion for any two wavelengths with respect to the base wavelengths F′ and C′. For example, the partial dispersion PdF for wavelengths d and F is defined by:PdF=(nd−nF)/((nF′−nC′).  (4)
Achromatic correction of a triplet is determined by the equation:Φ1/V1+Φ2/V2+Φ3/V3=0  (5)where                Φ1=the optical power of the first element,        V1=the Abbe number of the first element,        Φ2=the optical power of the second element,        V2=the Abbe number of the second element,        Φ3=the optical power of the third element, and        V3=the Abbe number of the third element.        
The condition for the triplet apochromatic correction is:P1(Φ1/V1)+P2(Φ2/V2)+P3(Φ3/V3)=0,  (6)Where                P3=partial dispersion of the third element.        
As ambient temperature conditions change, the shapes and positions of optical elements in a lens will change, and the focal length and position of an image formed by the lens will change as well. This is caused by glass expansion and changes in the glass refractive index with temperature. This dependence on temperature can have a significant impact on lens performance. So as to compensate for these changes, either the focal plane array has to be adjusted along the optical axis, or some elements inside the lens have to be moved. However, this approach is highly undesirable, because additional electronics and software are needed to perform and monitor the necessary adjustments.
On the other hand, a lens does not need thermal adjustment when the change of the focus position within the required temperature range stays inside the depth of focus of the lens. The diffraction depth of focus DOF is defined by:DOF=λ/NA2  (7)                where λ is the wavelength and NA is numerical aperture at the image space        
For λ=550 nm and F#4.5 (NA=0.111): DOF≈0.045 mm.
Therefore, in this example, if the lens design meets a requirement that all changes of the focus position over a specified range of temperature changes are inside 0.045 mm, no refocusing is required.
The Opto-thermal expansion coefficient β of an optical element is a property of the glass material, and it does not depend on the focal length or shape factor of the individual optics. For a single optical element:β=α+(dn/dT)/(n−1)  (8)                where        α=the thermal expansion coefficient of the glass        n=the refractive index of the glass at the current wavelength        T=temperaturethe change of the single element optical power Φ with temperature T is given by:dΦ/dT=(Φ)(−β).  (9)        
For an optical system comprising more than one optical element, the total change of the optical power Φsystem with temperature T is:dΦsystem/dT=−ΦsystemsΣ(Φi/Φsystem)(βi)  (10)where                Φi=optical power of a single element, and        βi=single element Opto-thermal expansion coefficient.        
Combining equations 2 and 10 allows design of an achromatic and athermalized doublet. Combining equations 2, 3 and 10 allows design of an athermalized doublet with a corrected secondary color (apochromatic correction).
Combining equations 5 and 10 allows design of an achromatic and athermalized triplet. Combining equations 5, 6 and 10 allows design of an athermalized apochromatic triplet.
Usually the partial dispersion of glasses has a linear dependence on a refractive index and Abbe number. The slope of a line connecting any two glasses determines the amount of a secondary spectrum in a doublet. The secondary spectrum can be reduced by using special glasses or materials with “abnormal” dispersion that varies non-linearly with the Abbe number, for example FK type glass (Schott) or SFPL (OHARA) or CaF2.
What is needed, therefore, is a compact, very low distortion, near-telecentric, athermalized lens that is suitable for airborne photography and mapping.